


from functools import reduce

snake_case				:			Dict	     = (
    """73167176531330624919225119674426574742355349194934"""
    """96983520312774506326239578318016984801869478851843"""
    """85861560789112949495459501737958331952853208805511"""
    """12540698747158523863050715693290963295227443043557"""
    """66896648950445244523161731856403098711121722383113"""
    """62229893423380308135336276614282806444486645238749"""
    """30358907296290491560440772390713810515859307960866"""
    """70172427121883998797908792274921901699720888093776"""
    """65727333001053367881220235421809751254540594752243"""
    """52584907711670556013604839586446706324415722155397"""
    """53697817977846174064955149290862569321978468622482"""
    """83972241375657056057490261407972968652414535100474"""
    """82166370484403199890008895243450658541227588666881"""
    """16427171479924442928230863465674813919123162824586"""
    """17866458359124566529476545682848912883142607690042"""
    """24219022671055626321111109370544217506941658960408"""
    """07198403850962455444362981230987879927244284909188"""
    """84580156166097919133875499200524063689912560717606"""
    """05886116467109405077541002256983155200055935729725"""
    """71636269561882670428252483600823257530420752963450"""
)






def 				__lowercase  (					__lowerCAmelCase				:							str = N  ):
							return max(
							    # mypy cannot properly interpret reduce
							    int(reduce(lambda __lowerCAmelCase   ,       __lowerCAmelCase  : str(int(__lowerCAmelCase  ) * int(__lowerCAmelCase  )  )   ,       n[i : i + 1_3]  )  )
							    for i in range(len(__lowerCAmelCase  ) - 1_2  )  )


if __name__ == "__main__":
						print(f"""{solution() = }""")






import torch

from diffusers import CMStochasticIterativeScheduler

from .test_schedulers import SchedulerCommonTest

class 							_UpperCamelCase					(       _A	):






			'''simple docstring'''

			__UpperCamelCase   :    Tuple          =			(CMStochasticIterativeScheduler,)
			__UpperCamelCase   :    List[str]          =			10

			def    lowerCAmelCase__						(							self			:							Optional[int]    ,						**snake_case_			:							List[str]   ):
							UpperCamelCase_:				Optional[int]						=    {
							    """num_train_timesteps""": 201,
							    """sigma_min""": 0.002,
							    """sigma_max""": 80.0,
							}

							config.update(**snake_case_   )
							return config

			def    lowerCAmelCase__						(							self			:							Tuple   ):
							UpperCamelCase_:				Tuple						=    10

							UpperCamelCase_:				Tuple						=    self.get_scheduler_config()
							UpperCamelCase_:				List[str]						=    self.scheduler_classes[0](**snake_case_   )

							scheduler.set_timesteps(snake_case_   )

							UpperCamelCase_:				int						=    scheduler.timesteps[0]
							UpperCamelCase_:				str						=    scheduler.timesteps[1]

							UpperCamelCase_:				Optional[int]						=    self.dummy_sample
							UpperCamelCase_:				int						=    0.1 * sample

							UpperCamelCase_:				Optional[Any]						=    scheduler.step(snake_case_    ,						snake_case_    ,						snake_case_   ).prev_sample
							UpperCamelCase_:				Any						=    scheduler.step(snake_case_    ,						snake_case_    ,						snake_case_   ).prev_sample

							self.assertEqual(output_a.shape    ,						sample.shape   )
							self.assertEqual(output_a.shape    ,						output_a.shape   )

			def    lowerCAmelCase__						(							self			:							Optional[Any]   ):
							for timesteps in [10, 50, 100, 1000]:
											self.check_over_configs(num_train_timesteps=snake_case_   )

			def    lowerCAmelCase__						(							self			:							Optional[Any]   ):
							for clip_denoised in [True, False]:
											self.check_over_configs(clip_denoised=snake_case_   )

			def    lowerCAmelCase__						(							self			:							Any   ):
							UpperCamelCase_:				Any						=    self.scheduler_classes[0]
							UpperCamelCase_:				List[str]						=    self.get_scheduler_config()
							UpperCamelCase_:				Tuple						=    scheduler_class(**snake_case_   )

							UpperCamelCase_:				Optional[int]						=    1
							scheduler.set_timesteps(snake_case_   )
							UpperCamelCase_:				Any						=    scheduler.timesteps

							UpperCamelCase_:				int						=    torch.manual_seed(0   )

							UpperCamelCase_:				Any						=    self.dummy_model()
							UpperCamelCase_:				Union[str, Any]						=    self.dummy_sample_deter * scheduler.init_noise_sigma

							for i, t in enumerate(snake_case_   ):
											# 1. scale model input
											UpperCamelCase_:				str						=    scheduler.scale_model_input(snake_case_    ,						snake_case_   )

											# 2. predict noise residual
											UpperCamelCase_:				List[Any]						=    model(snake_case_    ,						snake_case_   )

											# 3. predict previous sample x_t-1
											UpperCamelCase_:				str						=    scheduler.step(snake_case_    ,						snake_case_    ,						snake_case_    ,						generator=snake_case_   ).prev_sample

											UpperCamelCase_:				Union[str, Any]						=    pred_prev_sample

							UpperCamelCase_:				int						=    torch.sum(torch.abs(snake_case_   )   )
							UpperCamelCase_:				List[Any]						=    torch.mean(torch.abs(snake_case_   )   )

							assert abs(result_sum.item() - 192.7614   ) < 1e-2
							assert abs(result_mean.item() - 0.2510   ) < 1e-3

			def    lowerCAmelCase__						(							self			:							str   ):
							UpperCamelCase_:				Dict						=    self.scheduler_classes[0]
							UpperCamelCase_:				Tuple						=    self.get_scheduler_config()
							UpperCamelCase_:				List[Any]						=    scheduler_class(**snake_case_   )

							UpperCamelCase_:				str						=    [106, 0]
							scheduler.set_timesteps(timesteps=snake_case_   )
							UpperCamelCase_:				int						=    scheduler.timesteps

							UpperCamelCase_:				List[Any]						=    torch.manual_seed(0   )

							UpperCamelCase_:				List[Any]						=    self.dummy_model()
							UpperCamelCase_:				int						=    self.dummy_sample_deter * scheduler.init_noise_sigma

							for t in timesteps:
											# 1. scale model input
											UpperCamelCase_:				Optional[int]						=    scheduler.scale_model_input(snake_case_    ,						snake_case_   )

											# 2. predict noise residual
											UpperCamelCase_:				Dict						=    model(snake_case_    ,						snake_case_   )

											# 3. predict previous sample x_t-1
											UpperCamelCase_:				str						=    scheduler.step(snake_case_    ,						snake_case_    ,						snake_case_    ,						generator=snake_case_   ).prev_sample

											UpperCamelCase_:				List[str]						=    pred_prev_sample

							UpperCamelCase_:				Union[str, Any]						=    torch.sum(torch.abs(snake_case_   )   )
							UpperCamelCase_:				str						=    torch.mean(torch.abs(snake_case_   )   )

							assert abs(result_sum.item() - 347.6357   ) < 1e-2
							assert abs(result_mean.item() - 0.4527   ) < 1e-3

			def    lowerCAmelCase__						(							self			:							str   ):
							UpperCamelCase_:				int						=    self.scheduler_classes[0]
							UpperCamelCase_:				Optional[int]						=    self.get_scheduler_config()
							UpperCamelCase_:				Tuple						=    scheduler_class(**snake_case_   )

							UpperCamelCase_:				Any						=    [39, 30, 12, 15, 0]

							with self.assertRaises(snake_case_    ,						msg="""`timesteps` must be in descending order."""   ):
											scheduler.set_timesteps(timesteps=snake_case_   )

			def    lowerCAmelCase__						(							self			:							str   ):
							UpperCamelCase_:				Union[str, Any]						=    self.scheduler_classes[0]
							UpperCamelCase_:				Tuple						=    self.get_scheduler_config()
							UpperCamelCase_:				List[str]						=    scheduler_class(**snake_case_   )

							UpperCamelCase_:				Tuple						=    [39, 30, 12, 1, 0]
							UpperCamelCase_:				List[Any]						=    len(snake_case_   )

							with self.assertRaises(snake_case_    ,						msg="""Can only pass one of `num_inference_steps` or `timesteps`."""   ):
											scheduler.set_timesteps(num_inference_steps=snake_case_    ,						timesteps=snake_case_   )




			def    lowerCAmelCase__						(							self			:							int   ):
							UpperCamelCase_:				Any						=    self.scheduler_classes[0]
							UpperCamelCase_:				int						=    self.get_scheduler_config()
							UpperCamelCase_:				int						=    scheduler_class(**snake_case_   )

							UpperCamelCase_:				int						=    [scheduler.config.num_train_timesteps]

							with self.assertRaises(
							    snake_case_    ,						msg="""`timesteps` must start before `self.config.train_timesteps`: {scheduler.config.num_train_timesteps}}"""    ,						):
											scheduler.set_timesteps(timesteps=snake_case_   )






